Download Modelling Here major steps are needed

Centrum voor Wiskunde en Informatica
A Scientific Computing Framework
for Studying Axon Guidance
Jan Verwer
CWI and
Univ. of Amsterdam
Computational Neuroscience Meeting, NWO, December 9, 2005
Scientific Computing
Scientific Computing
Computer based applied mathematics
Scientific Computing
Computer based applied mathematics, involving
• Modelling
• Analysis
• Simulation
Scientific Computing
Computer based applied mathematics, involving
• Modelling Prescription of a given problem in formulas,
relations, equations. Approximating reality.
Here the application is prominent.
• Analysis
• Simulation
Scientific Computing
Computer based applied mathematics, involving
• Modelling Prescription of a given problem in formulas,
relations, equations. Approximating reality.
Here the application is prominent.
• Analysis
• Simulation
Study of mathematical and numerical issues
(stability, conservation rules, etc).
Here the mathematics is prominent.
Scientific Computing
Computer based applied mathematics, involving
• Modelling Prescription of a given problem in formulas,
relations, equations. Approximating reality.
Here the application is prominent.
• Analysis
Study of mathematical and numerical issues
(stability, conservation rules, etc).
Here the mathematics is prominent.
• Simulation Programming, benchmark selection, testing,
visualization, interpretation.
Here the computer is prominent.
Scientific Computing
Computer based applied mathematics, involving
• Modelling Prescription of a given problem in formulas,
relations, equations. Approximating reality.
Here the application is prominent.
• Analysis
Study of mathematical and numerical issues
(stability, conservation rules, etc).
Here the mathematics is prominent.
• Simulation Programming, benchmark selection, testing,
visualization, interpretation.
Here the computer is prominent.
Scientific Computing
Computer based applied mathematics, involving
• Modelling
This is critical.
• Analysis
This is fun.
• Simulation
This is hard work.
Axon Guidance
Axon Guidance
Results from the PhD thesis of J. Krottje (CWI):
On the numerical solution of diffusion systems with
localized, gradient-driven moving sources, UvA,
November 17, 2005
Axon Guidance
Results from the PhD thesis of J. Krottje (CWI):
On the numerical solution of diffusion systems with
localized, gradient-driven moving sources, UvA,
November 17, 2005
Joint project between CWI (Verwer), NIBR (van Pelt)
and VU (van Ooyen), carried out at CWI and funded by
Axon Guidance
Axon Guidance
Axon Guidance Modelling
Axon Guidance Modelling
Axon Guidance Modelling
A first PDE model was built
by Hentschel & van Ooyen ‘99
The model moves particles (axon heads)
in attractant-repellent gradient fields
Axon Guidance Modelling
A first PDE model was built
by Hentschel & van Ooyen ‘99
The model moves particles (axon heads)
in attractant-repellent gradient fields
Axon Guidance Modelling
A first PDE model was built
by Hentschel & van Ooyen ‘99
The model moves particles (axon heads)
in attractant-repellent gradient fields
Axon Guidance Modelling
A first PDE model was built
by Hentschel & van Ooyen ‘99
The model moves particles (axon heads)
in attractant-repellent gradient fields
Krottje generalized their model and has
developed the Matlab package: AG-tools
Axon Guidance Modelling
Mathematical Framework
Mathematical Framework
Three basic ingredients
• Domain
• States
• Fields
Mathematical Framework
Three basic ingredients
• Domain
• States
• Fields
Physical environment of axons, neurons,
chemical fields. Domain in 2D with smooth
complicated boundary, possibly with holes.
Mathematical Framework
Three basic ingredients
• Domain
Physical environment of axons, neurons,
chemical fields. Domain in 2D with smooth
complicated boundary, possibly with holes.
• States
Growth cones, target cells, axon properties,
locations. Particle dynamics modelled by
ordinary differential equations.
• Fields
Mathematical Framework
Three basic ingredients
• Domain
Physical environment of axons, neurons,
chemical fields. Domain in 2D with smooth
complicated boundary, possibly with holes.
• States
Growth cones, target cells, axon properties,
locations. Particle dynamics modelled by
ordinary differential equations.
• Fields
Changing concentrations of guidance molecules
due to diffusion, absorption, moving sources.
Modelled by partial differential equations.
Mathematical Framework
Three basic ingredients
• Domain
• States
• Fields
Mathematical Framework
Three basic ingredients
• Domain
• States
• Fields
Mathematical Framework
Three basic ingredients
• Domain
• States
• Fields
Mathematical Framework
Three basic ingredients
• Domain
• States
• Fields
- Local function
approximations
- Arbitrary node sets
- Unstructured
Voronoi grids
- Local refinement
- Implicit-explicit
Runge-Kutta
integration
AGTools Example
AGTools Example
Ilustration of topographic mapping with 5 guidance fields
(3 diffusive and 2 membrane bound) and 200 growth cones
Topographic Mapping Equations
Topographic Mapping Equations
No hard laws.
Phenomenal setup.
Neuro Scientific Computing Challenges
• Modelling
• Analysis
• Simulation
Neuro Scientific Computing Challenges
• Modelling
• Analysis
• Simulation
Here major steps are needed:
Neuro Scientific Computing Challenges
• Modelling
Here major steps are needed:
- e.g., dimensioned wires instead of point
particles,
- in general, a less phenomenal setup,
- realistic data (coefficients, parameters).
• Analysis
• Simulation
Neuro Scientific Computing Challenges
• Modelling
Here major steps are needed:
- e.g., dimensioned wires instead of point
particles,
- in general, a less phenomenal setup,
- realistic data (coefficients, parameters).
• Analysis
• Simulation
Higher modelling level will require
participation of PDE analysts.
Neuro Scientific Computing Challenges
• Modelling
Here major steps are needed:
- e.g., dimensioned wires instead of point
particles,
- in general, a less phenomenal setup,
- realistic data (coefficients, parameters).
• Analysis
Higher modelling level will require
participation of PDE analysts.
• Simulation 3D-model with many species and axons.
Will require huge computer resources,
and presumably a different grid approach.